Heat oven to 375 degrees F. In 12-inch nonstick skillet with ovenproof handle (see Note), heat oil over medium-high heat. Add onion; sauté 2 minutes. Add potatoes, asparagus, mushrooms, salt and pepper; cook, stirring occasionally, 10 minutes.
In medium bowl, with whisk, lightly beat eggs, Parmesan cheese and rosemary. Stir egg mixture and chopped ham into vegetables; cook 3 minutes. Place in heated oven; bake 10 minutes. Sprinkle top with mozzarella cheese. Bake 5 minutes more until egg is set and cheese is melted. Serve with salad, if desired.
